Method and Apparatus for Determining Cardiac Performance in a Patient

ABSTRACT

An apparatus for determining heart transplant rejection of a heart in a patient includes at least two electrodes adapted to be sewn into the heart that span the left ventricle. The apparatus includes a voltage generator adapted to be inserted in the patient which generates a voltage to the two electrodes and senses the resulting voltage from the two electrodes. A method for determining heart transplant rejection of a heart in a patient. A pacemaker for a patient (including bi-ventricular pacing and AICDs). The pacemaker includes an RV lead having four electrodes adapted to be inserted into the RV apex. The pacemaker includes a voltage generator which generates a voltage signal to the electrodes and senses the instantaneous voltage along the length of the RV and determines the real and imaginary components to remove the myocardial components of the septum and RV free wall to determine absolute RV blood volume. The pacemaker includes a battery connected to the voltage generator. The pacemaker includes a defibrillator connected to the battery. The pacemaker can also be a bi-ventricular pacemaker to restore RV and LV synchrony during contraction. A method for assisting a heart of a patient.

FIELD OF THE INVENTION

The present invention is related to measuring instantaneous ventricularvolume in the heart of a patient. More specifically, the presentinvention is related to measuring instantaneous ventricular volume inthe heart of a patient by removing the contributor to conductance ofmuscle, and applying a non-linear relationship to the measuredconductance and the volume of blood in the heart including a failingdilated heart (either right or left ventricle) with reduced function andmay have an Automatic Implantable Cardiac Defibrillator (AICD) and/orpacemaker. The present invention also allows determination of hearttransplant rejection by telemetry to avoid the use of myocardial biopsy.

BACKGROUND OF THE INVENTION

Measurements of electrical conductance using a tetrapolar admittancecatheter are used to estimate instantaneous ventricular volume inanimals and humans. The measurements of volume are plotted againstventricular pressure to determine several important parameters ofcardiac physiologic function. A significant source of uncertainty in themeasurement is parallel conductance due to current in the ventricularmuscle. The estimated volume is larger than the blood volume alone,which is required for the diagnostic measurement. Furthermore,presently, a linear relationship between conductance and estimatedvolume is used to calibrate the measurements. The actual relationship issubstantially nonlinear.

The invention comprises an improved method for estimating instantaneousblood volume in a ventricle by subtracting the muscle contribution formthe total conductance measured. The method relies on measuring thecomplex admittance, rather than apparent conductance (admittancemagnitude), as is presently done. Briefly, the improvement consists ofmeasuring the phase angle in addition to admittance magnitude and thendirectly subtracting the muscle component from the combined measurement,thereby improving the estimate of instantaneous blood volume. Thetechnique works because the electrical properties of muscle arefrequency-dependent, while those of blood are not. This calibrationtechnique is a substantial improvement in clinical and researchinstrumentation calibration methods.

The invention comprises an improved method for estimating instantaneousvolume of a ventricle by applying a nonlinear relationship between themeasured conductance and the volume of blood in the surrounding space.The nonlinear calibration relation has been determined from experimentsand numerical model studies. This calibration technique is a substantialimprovement in clinical and research instrumentation calibrationmethods.

SUMMARY OF THE INVENTION

The present invention pertains to an apparatus for determining cardiacperformance or volume in the patient. The apparatus comprises aconductance (admittance) catheter for measuring conductance and bloodvolume in a heart chamber of the patient. The apparatus comprises aprocessor for determining instantaneous volume of the ventricle byapplying a non-linear relationship between the measured conductance andthe volume of blood in the heart chamber to identify mechanical strengthof the chamber. The processor is in communication with the conductance(admittance) catheter.

The present invention pertains to a method for determining cardiacperformance in the patient. The method comprises the steps of measuringconductance and blood volume in a heart chamber of the patient with aconductance catheter. There is the step of determining instantaneousvolume of the ventricle by applying a non-linear relationship betweenthe measured conductance and the volume of blood in the heart chamber toidentify mechanical strength of the chamber with a processor as well asthe volume of that chamber. The processor in communication with theconductance (admittance) catheter.

The present invention pertains to an apparatus for determining cardiacperformance in a patient. The apparatus comprises a conductance(admittance) catheter for measuring conductance in a heart chamber ofthe patient, where the conductance includes contributions from blood andmuscle with respect to the heart chamber. The apparatus comprises aprocessor for determining instantaneous volume of the heart chamber byremoving the muscle contribution from the conductance. The processor isin communication with the conductance (admittance) catheter.

The present invention pertains to a method for determining cardiacperformance in a patient. The method comprises the steps of measuringconductance in a heart chamber of the patient with a conductance(admittance) catheter, where the conductance includes contributions fromblood and muscle with respect to the heart chamber. There is the step ofdetermining instantaneous volume of the heart chamber by removing themuscle contribution from the conductance with a processor, the processorin communication with the conductance catheter.

The present invention pertains to an apparatus for determining cardiacperformance in the patient. The apparatus comprises a conductance(admittance) catheter having measuring electrodes for measuringconductance in a heart chamber of the patient. The apparatus comprises aprocessor for determining instantaneous volume of the heart chamberaccording to

${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$

where: β(G)=the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L isdistance between measuring electrodes, and Y_(p)=the parallel leakageadmittance, dominated by cardiac muscle, the processor in communicationwith the conductance catheter.

The present invention pertains to a method for determining cardiacperformance in the patient. The method comprises the steps of measuringconductance and blood volume in a heart chamber of the patient with aconductance (admittance) catheter having measuring electrodes. There isthe step of determining instantaneous volume of the ventricle accordingto

${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$

where: β(G)=the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L isdistance between measuring electrodes, and Y_(p) the parallel leakageadmittance, dominated by cardiac muscle, to identify mechanical strengthof the chamber with a processor. The processor is in communication withthe conductance (admittance) catheter.

The present invention pertains to an apparatus for determining hearttransplant rejection of a heart in a patient. The apparatus comprises atleast two electrodes adapted to be sewn into the heart that span theleft ventricle. The apparatus comprises a voltage generator adapted tobe inserted in the patient which generates a voltage to the twoelectrodes and senses the resulting voltage from the myocardium todetermine if the electrical properties of the myocardium have changeddue to rejection, in place of the current standard of myocardial biopsy.

The present invention pertains to a method for determining hearttransplant rejection of a heart in a patient. The method comprises thesteps of sewing into the heart at least two electrodes that span theleft ventricle. There is the step of inserting in the patient a voltagegenerator which generates a voltage to the two electrodes and senses theresulting voltage from the myocardium.

The present invention pertains to a pacemaker for a patient. The type ofpacemaker can include a bi-ventricular pacemaker for resynchronizationtherapy. The pacemaker comprises in part an RV lead having fourelectrodes which span the RV chamber and are adapted to be inserted intothe RV apex with at least one of the four electrodes placed in eitherthe right atrium or veins drawing into the right heart of the patient.The pacemaker comprises a voltage generator which generates a voltagesignal to the electrodes and senses the instantaneous voltage in the RVand determines the real and imaginary components to remove themyocardial component from the septum and RV free wall to determineabsolute RV blood volume. The pacemaker comprises a battery connected tothe voltage generator. The pacemaker comprises a defibrillator connectedto the battery, and/or a bi-ventricular pacemaker for resynchronizationtherapy.

The present invention pertains to a method for assisting a heart of apatient. The method comprises the steps of inserting into the RV apex anRV lead of a pacemaker/bi-ventricular pacemaker and/or AICD having fourelectrodes that span the length of the RV. There is the step ofgenerating a voltage signal to the electrodes from a voltage generator.There is the step of sensing the instantaneous voltage in the RV withthe voltage generator to determine the real and imaginary components ofthe voltage to remove the myocardial component from the septum and RVfree wall to determine absolute RV blood volume, or rather than removeit, focus on the signal from the septum and RV free wall to determine ifmyocardial rejecting is occurring as in the case of a transplantedheart.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings, the preferred embodiment of the inventionand preferred methods of practicing the invention are illustrated inwhich:

FIG. 1 shows a four electrode catheter in volume cuvette.

FIG. 2 is a plot for estimating parallel conductance.

FIG. 3 is a plot of apparent conductivity of cardiac muscle as afunction of frequency in CD1 mice in vivo at 37° C.

FIG. 4 shows a circuit diagram of a catheter and a measurement systemfor an open circuit load. The small triangles are the common node forthe instrument power supply.

FIG. 5 is a plot of catheter phase effects for saline solutions from 720to 10,000 μS/cm from 1 kHz to 1 MHz. Apparent conductivity (|η|) ofsaline solutions (μS/cm).

FIG. 6 is a plot of conductance vs. volume in mouse-sized calibrationcuvette.

FIG. 7 is a schematic representation of the apparatus of the presentinvention.

FIG. 8 is a cylinder-shaped murine LV model: both blood and myocardiumare modeled as cylinders.

FIG. 9 is a comparison between true volume and estimated volume by thenew and Baan's equations in FEMLAB simulations.

FIG. 10 is a comparison between true volume and estimated volume usingthe new and Baan's equations in saline experiments.

FIG. 11 is a representation of an apparatus for determining hearttransplant rejection of a heart in a patient of the present invention.

FIG. 12 is a representation of a penetrating transducer of the presentinvention.

FIG. 13 is a representation of a bottom view of a surface transducer ofthe present invention.

FIG. 14 is a representation of a side view of the surface transducer.

FIG. 15 is a representation of the various embodiments of the presentinvention as applied to the heart.

FIG. 16 is a representation of a first embodiment regarding possibleplacement of the apparatus for determining heart transplant rejection.

FIG. 17 is a representation of an alternative placement of electronicinstrumentation regarding the apparatus for determining heart transplantrejection.

FIG. 18 is a representation of a pacemaker for a patient according tothe present invention.

DETAILED DESCRIPTION

Referring now to the drawings wherein like reference numerals refer tosimilar or identical parts throughout the several views, and morespecifically to FIG. 7 thereof, there is shown an apparatus fordetermining cardiac performance in the patient. The apparatus comprisesa conductance (admittance) catheter 12 for measuring conductance andblood volume in a heart chamber of the patient. The apparatus comprisesa processor 14 for determining instantaneous volume of the ventricle byapplying a non-linear relationship between the measured conductance andthe volume of blood in the heart chamber to identify mechanical strengthof the chamber. The processor 14 is in communication with theconductance catheter 12.

Preferably, the apparatus includes a pressure sensor 16 for measuringinstantaneous pressure of the heart chamber in communication with theprocessor 14. The processor 14 preferably produces a plurality ofdesired wave forms at desired frequencies for the conductance(admittance) catheter 12. Preferably, the processor 14 produces theplurality of desired wave forms at desired frequencies simultaneously,and the processor 14 separates the plurality of desired wave forms atdesired frequencies the processor 14 receives from the conductance(admittance) catheter 12. The conductance (admittance) catheter 12preferably includes a plurality of electrodes 18 to measure a least onesegmental volume of the heart chamber.

Preferably, the non-linear relationship depends on a number of theelectrodes 18, dimensions and spacing of the electrodes 18, and anelectrical conductivity of a medium in which the electrodes 18 of thecatheter 12 are disposed. The non-linear relationship may be expressedas (or a substantially similar mathematical form):

β(G)(σ=0.928S/m)=1+1.774(10^(7.481×10) ⁻⁴ ^((G−2057)))

Alternatively, an approximate calibration factor may be used withsimilar accuracy of the form (or its mathematical equivalent):

β≈e^(γG) ^(h) ²

where: G is the measured conductance (S), the calculations have beencorrected to the conductivity of whole blood at body temperature (0.928S/m), and 2057 is the asymptotic conductance in μS when the cuvette isfilled with a large volume of whole blood. Preferably,

${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$

where: β(G)=the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L isdistance between measuring electrodes, and Y_(p)=the parallel leakageadmittance, dominated by cardiac muscle.

The pressure sensor 16 preferably is in contact with the conductance(admittance) catheter 12 to measure ventricular pressure in the chamber.Preferably, the plurality of electrodes 18 includes intermediateelectrodes 20 to measure the instantaneous voltage signal from theheart, and outer electrodes 22 to which a current is applied from theprocessor 14. The pressure sensor 16 preferably is disposed between theintermediate electrodes 20. Preferably, the processor 14 includes acomputer 24 with a signal synthesizer 26 which produces the plurality ofdesired wave forms at desired frequencies and a data acquisitionmechanism 28 for receiving and separating the plurality of desired waveforms at desired frequencies. The computer 24 preferably convertsconductance into a volume. Preferably, the computer 24 produces a drivesignal having a plurality of desired wave forms at desired frequenciesto drive the conductance (admittance) catheter 12.

The present invention pertains to a method for determining cardiacperformance in the patient. The method comprises the steps of measuringconductance and blood volume in a heart chamber of the patient with aconductance (admittance) catheter 12. There is the step of determininginstantaneous volume of the ventricle by applying a non-linearrelationship between the measured conductance and the volume of blood inthe heart chamber to identify mechanical strength of the chamber with aprocessor 14. The processor 14 in communication with the conductance(admittance) catheter 12.

Preferably, there is the step of measuring instantaneous pressure of theheart chamber with a pressure sensor 16 in communication with theprocessor 14. There is preferably the step of producing a plurality ofdesired wave forms at desired frequencies for the conductance(admittance) catheter 12. Preferably, the producing step includes thestep of producing the plurality of desired wave forms at desiredfrequencies simultaneously, and including the step of the processor 14separating the plurality of desired wave forms at desired frequenciesthe processor 14 received from the conductance catheter 12. Theproducing step preferably includes the step of producing with theprocessor 14 the plurality of desired wave forms at desired frequenciessimultaneously.

Preferably, the determining step includes the step of applying thenon-linear relationship according to the following (or its mathematicalequivalent):

β(G)(σ=0.928S/m)=1+1.774(10^(7.489×10) ⁻⁴ ^((G−2057)))

where: G is the measured conductance (S), the calculations have beencorrected to the conductivity of whole blood at body temperature (0.928S/m), and 2057 is the asymptotic conductance in μS when the cuvette isfilled with a large volume of whole blood. Or, alternatively, anapproximate geometry calibration factor may be used:

β=e^(γ[G) ^(b) ^(]) ²

where α is determined experimentally or from mathematical calculationsor numerical models.

The determining step preferably includes the step of determininginstantaneous volume according to

${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$

where: β(G) the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L isdistance between measuring electrodes, and Y_(p)=the parallel leakageadmittance, dominated by cardiac muscle.

Preferably, the step of measuring instantaneous pressure includes thestep of measuring instantaneous pressure with the pressure sensor 16 incontact with the conductance (admittance) catheter 12 to measure theventricular pressure in the chamber. The measuring step preferablyincludes the step of measuring at least one segmental volume of theheart chamber with a plurality of electrodes 18 on the conductance(admittance) catheter 12. Preferably, the measuring step includes thesteps of applying a current to outer electrodes 22 of the plurality ofelectrodes 18 from the processor 14, and measuring an instantaneousvoltage signal from the heart with intermediate electrodes 20 of theplurality of electrodes 18.

The step of measuring instantaneous pressure preferably includes thestep of measuring instantaneous pressure with the pressure sensor 16disposed between the intermediate electrodes 20 and the outer electrodes22. Preferably, the producing with the processor 14 step includes thestep of producing with a signal synthesizer 26 of a computer 24 theplurality of desired wave forms at desired frequencies, and theprocessor 14 separating step includes the step of receiving andseparating the plurality of desired wave forms at desired frequencieswith a data acquisition mechanism 28 of the computer 24. There ispreferably the step of converting conductance into a volume with thecomputer 24. Preferably, there is the step of producing with thecomputer 24 a drive signal having the plurality of desired wave forms atdesired frequencies to drive the conductance (admittance) catheter 12.

The present invention pertains to an apparatus for determining cardiacperformance in a patient. The apparatus comprises a conductance(admittance) catheter 12 for measuring conductance in a heart chamber ofthe patient, where the conductance includes contributions from blood andmuscle with respect to the heart chamber. The apparatus comprises aprocessor 14 for determining instantaneous volume of the heart chamberby removing the muscle contribution from the conductance. The processor14 is in communication with the conductance catheter 12.

Preferably, the apparatus includes a pressure sensor 16 for measuringinstantaneous pressure of the heart chamber in communication with theprocessor 14. The processor 14 preferably produces a plurality ofdesired wave forms at desired frequencies for the conductance(admittance) catheter 12. Preferably, the processor 14 produces theplurality of desired wave forms at desired frequencies simultaneously,and the processor 14 separates the plurality of desired wave forms atdesired frequencies the processor 14 receives from the conductance(admittance) catheter 12. The processor 14 preferably measures complexadmittance with the conductance (admittance) catheter 12 to identify themuscle contribution.

Preferably, the complex admittance is defined as

Y _(p) =Gm+jωCm (Y subscript p)

where

Cm capacitance component of muscle (F=Farads) (C subscript m)

ω=angular frequency (radians/second) (greek “omega”=2 pi f)

Gm=conductance of muscle (S=Siemens) (G subscript m). The conductancepreferably is defined as

Y(t)=Gb+Gm+jωCm

where Gb=conductance of blood (S) (G subscript b).

The present invention pertains to a method for determining cardiacperformance in a patient. The method comprises the steps of measuringconductance in a heart chamber of the patient with a conductance(admittance) catheter 12, where the conductance includes contributionsfrom blood and muscle with respect to the heart chamber. There is thestep of determining instantaneous volume of the heart chamber byremoving the muscle contribution from the conductance with a processor14, the processor 14 in communication with the conductance (admittance)catheter 12.

Preferably, there is the step of measuring instantaneous pressure of theheart chamber with a pressure sensor 16 in communication with theprocessor 14. There is preferably the step of producing a plurality ofdesired wave forms at desired frequencies for the conductance(admittance) catheter 12. Preferably, the producing step includes thestep of producing the plurality of desired wave forms at desiredfrequencies simultaneously, and including the step of the processor 14separating the plurality of desired wave forms at desired frequenciesthe processor 14 received from the conductance catheter 12. Theproducing step preferably includes the step of producing with theprocessor 14 the plurality of desired wave forms at desired frequenciessimultaneously. Preferably, there is the step of measuring complexadmittance with the conductance catheter 12 to identify the musclecontribution.

The measuring the complex admittance step preferably includes the stepof measuring the complex admittance according to

Yp=Gm+jωCm (Y subscript p)

where

Cm=capacitance component of muscle (F=Farads) (C subscript m)

ω=angular frequency (radians/second) (greek “omega”=2 pi f)

Gm=conductance of muscle (S=Siemens) (G subscript m).

Preferably, the determining step includes the step of determininginstantaneous volume based on conductance defined as

Y(t)=Gb+Gm+jωCm

where Gb=conductance of blood (S) (G subscript b).

The present invention pertains to an apparatus for determining cardiacperformance in the patient. The apparatus comprises a conductance(admittance) catheter 12 for measuring conductance in a heart chamber ofthe patient. The apparatus comprises a processor 14 for determininginstantaneous volume of the heart chamber according to

${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$

where: β(G)=the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L isdistance between measuring electrodes, and Y_(p)=the parallel leakageadmittance, dominated by cardiac muscle, the processor 14 incommunication with the conductance catheter 12.

The present invention pertains to a method for determining cardiacperformance in the patient. The method comprises the steps of measuringconductance and blood volume in a heart chamber of the patient with aconductance (admittance) catheter 12. There is the step of determininginstantaneous volume of the ventricle according to

${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$

where: β(G) the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L isdistance between measuring electrodes, and Y_(p)=the parallel leakageadmittance, dominated by cardiac muscle, to identify mechanical strengthof the chamber with a processor 14. The processor 14 is in communicationwith the conductance catheter 12.

The classic means to determine left ventricular pressure-volume (PV)relationships in patients on a beat-by-beat basis is through the use ofthe conductance (volume/admittance) catheter 12. The electric field thatit creates in the human left or right ventricle at the time of heartcatheterization is the only technology capable of measuringinstantaneous left and/or right ventricular volume during maneuvers suchas transient occlusion of the inferior vena cava. Such maneuvers allowdetermination of the wealth of information available from the PV planeincluding: end-systolic elastance, diastolic compliance, and effectivearterial elastance. However, use of conductance technology in patientswith dilated hearts whose LV volumes can range from 200 to 500 ml hasbeen problematic.

The G-V method measures the conductance between electrodes 18 located inthe LV and aorta. A minimum of four electrodes 18 is required to preventthe series impedance of the electrode-electrolyte interfaces fromdistorting the measurement. Typically, the two current source-sinkelectrodes are located in the aorta and in the LV near the apex(electrodes 1 and 4 in FIG. 1). The potential difference between thepotential measuring electrodes (2 and 3) is used to calculate theconductance: G=I/V. The governing assumption is that the current densityfield is sufficiently uniform that the volume and conductance are simplyrelated by Baan's equation [1]:

$\begin{matrix}{{{Vol}(t)} = {{\left\lbrack \frac{1}{\alpha} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{G(t)} - G_{p}} \right\rbrack}} & (1)\end{matrix}$

where: α is the geometry factor (a dimensionless constant), L is thecenter-to-center distance between voltage sensing electrodes (2 and 3)(m), σ_(b) is the conductivity of blood (S/m), G(t) is the measuredinstantaneous conductance (S), and G_(p) is the parallel conductance (S)in cardiac muscle (G_(p)=0 in the calibration cuvette of FIG. 1).

Two limitations inherent in the state-of-the-art technique interferewith accurate measurements: 1) the electric field around the sensingelectrodes 18 is not uniform, leading to a non-linear relationshipbetween measured conductance and ventricular volume which has decidedlylower sensitivity to large volumes, and 2) the parallel conductancesignal added by surrounding cardiac muscle adds virtual volume to themeasurement. The new technique improves the estimate of the parallelmuscle conductance based on the measurement of complex admittance at twoor more frequencies, rather than using the admittance magnitude, as ispresently done. Furthermore, the inherent non-linearity of conductancevs. volume is usually compensated by establishing a piece-wise linearapproximation to the sensitivity curve (Vol vs. G) in the region ofoperation. That is, α is actually a function of the diameter of thevolume in FIG. 1; but is assumed constant over the operating range of ameasurement, ESV to EDV.

The electrical properties of cardiac muscle are frequency-dependent[6-14] while those of blood are not [15-18]. The admittance measurementat (at least) one frequency can be used to separate the muscle componentfrom the combined muscle-blood signal. Measurement of the phase angle ofthe admittance is a more sensitive indicator of the muscle signal thanthe magnitude of the admittance, which is currently measured.Information contained in the phase angle can improve the overallaccuracy of the single and/or dual frequency admittance system. Thisreformulation of the measurement allows one to verify that the effectivesensing volume actually reaches the ventricular muscle in the case of anenlarged heart.

In the operation of the invention, the parallel conductance signal ispresently compensated by three methods: 1) hypertonic saline injection[19, 20], 2) occlusion of the inferior vena cava (IVC) [21], and 3)conductance measurement at one or two frequencies [22, 23]. In the firstapproach, a known volume of hypertonic saline (usually 10% NaCl) isinjected and the beat-by-beat conductance signal measured as it washesthrough the LV during several beats. The End Diastolic Conductance (EDG)is plotted against End Systolic Conductance (ESG), and the resultingline is projected back to the line of equal values (EDG=ESG when strokevolume=0), and the remainder is the estimate of parallel conductance,G_(p). (see FIG. 2.). In the second approach, occlusion of the IVC,shrinks the LV volume, but the result is analyzed in the same way asFIG. 2. The third approach attempted to use the frequency dependence ofmuscle to identify the parallel conductance [22, 23]. This is similar tothe approach described here, but different in that the particularfrequencies were limited to a maximum of about 30 kHz and only themagnitude of the combined signal was used. A maximum frequency of 100kHz is used here to better separate the muscle from the combined signal;further, the phase angle is a much more sensitive indicator of musclethan admittance magnitude alone. Also, the use of the phase angle andmagnitude of the admittance-signal allows as few as a single frequencyto be utilized in an accurate fashion, not possible with a singlefrequency magnitude device.

Each of the parallel conductance compensation approaches has undesirablefeatures. Hypertonic saline injection creates an aphysiologicelectrolyte load that is undesirable in the failing heart. IVC occlusionbrings the ventricular free wall and septum closer to the electrodearray and artificially elevates the parallel conductance. The dualfrequency magnitude only measurements are able to identify a differencesignal between blood and cardiac muscle, but measurement using themagnitude of admittance alone is not sufficiently sensitive to yieldsatisfying results, and the particular frequencies used in the past arenot the best to separate the two signals. Further, the use of phaseangle and magnitude of the admittance signal alone can be performedaccurately using a single frequency. There are other considerations inthe dual-frequency magnitude only measurement which affect overallaccuracy—notably the parasitic impedances in the catheter 12itself—which must be compensated before reliable calculations may bemade. The present invention is a significant improvement to the dualfrequency magnitude only method; it uses measurements of the complexadmittance to more accurately identify the parallel muscle volume signaland does not require injecting fluids or changing the LV volume tocomplete.

Frequency Dependence of Muscle Electrical Properties: Electrolyticsolutions, blood and all semiconducting materials have an electricalconductivity, σ, that is essentially independent of frequency.Dielectric materials have an electric permittivity, ∈ (F/m): in essence,permittivity is a measure of the polarizable dipole moment per unitvolume in a material [14]. A general material has both semiconductingand dielectric properties, and each aspect contributes to the totalcurrent density vector, J_(tot) (A/m²) in a vector electric field, E(V/m). The conductivity, σ, results in conduction current densityaccording to Ohm's Law, and the permittivity, ∈, contributes“displacement” current density in a harmonic (i.e. sinusoidal) electricfield, as reflected in the right hand side of Ampere's Law [40]:

J _(tot)=(σ+jω∈)E  (2)

where: j=√{square root over (−1)} and ω=2πf=the angular frequency (r/s).J_(tot) is complex even if E is real—in other words, J and E are not inphase with each other unless ω∈ is small with respect to σ. Most alltissues behave as semiconductors at all frequencies below about 10 MHzbecause σ>>ω∈. The remarkable exception is muscle tissue in vivo or veryfreshly excised, [10-12, and our own unpublished measurements]. Tocalibrate this discussion, water has a very strong dipole moment, andhas a relative permittivity of around 80 at frequencies below about 1MHz; and the relative permittivities of most tissues are, therefore,usually dominated by their water content. Muscle, in contrast, has avery high relative permittivity: around 16,000 in the 10 kHz to 100 kHzrange (almost 200 times that of water) [11], owing to the trans-membranecharge distribution. Consequently, ω∈ are able to observe the frequencydependence of muscle total current density since ω∈ is larger than a forfrequencies above about 15 kHz.

For example, the apparent conductivity of murine cardiac muscle using asurface tetrapolar probe shows a reliable and repeatable frequencydependence. In FIG. 3, the indicated conductivity increasessignificantly above about 10 kHz. The conductivity in the figureincludes some permittivity effects: the measurement device actuallyindicates the magnitude of the (σ+jω∈) term in equation 2. For muscle,it is more accurate to think in terms of “admittivity”, η=σ+jω∈. σ=1,800μS/cm (0.18 S/m) from the low frequency portion of the plot, andestimate that ∈=16,000 ∈₀ (F/m) which compares well with published data.In the figure, the parasitic capacitances of the surface probe have beencompensated out using measurements of the surface probe on electrolyticsolutions with the same baseline conductivity as muscle.

Numerical Model Studies: Numerical models of the murine catheter in amouse LV were executed at volumes representative of the normal ESV andEDV in the mouse. The numerical model was an enhanced version of themodel used for the cuvette studies: each control volume (CV) could beassigned a different value of electrical conductivity, σ. The modelspatial resolution and FDM calculational approach were the same asdescribed above. A larger number of iterations were required forconvergence, however, around 400,000 iterations. This is because theelectrical boundary conditions of the inhomogeneous media substantiallyincrease the number of trials required to settle to the final solution.Models were completed using realistic volumes for ESV and EDV derivedfrom conductance catheter 12 data: 19 μl and 45 μl, respectively(ejection fraction=60%). Electrical conductivities for blood, cardiacmuscle and aorta were: σ_(b)=0.928 S/m, σ_(m)=0.0945 S/m at 10 kHz and0.128 S/m at 100 kHz, σ_(a)=0.52 S/m [41], respectively. All of theproperties are real-valued in the model—the complex nature of muscle hasnot been included in the preliminary studies. The ventricular free wallendocardial surface was treated as a smooth ellipse, and the LV wasmodeled as an ellipsoid of revolution. The geometry was considerablysimplified over the actual LV for two reasons: 1) the purpose of themodel was to identify the expected order-of-magnitude of musclecontribution to the measured conductance, 2) the resources and timeavailable did not permit development of a detailed 3-D geometry, nor theuse of more accurate finite element method (FEM) models.

Table 1 compares FDM model and experiment data. The model consistentlyunder-estimates the measured conductances: by about 11% and 35% at 10kHz, and by 30% and 47% at 100 kHz. The comparisons at 10 kHz are leastsensitive to uncertainty in tissue electrical properties and catheter 12effects. Deviations at this frequency are more likely due to geometricsimplifications in the model and under-estimation of the appropriate LVvolume to use.

TABLE 1 Summary of model and experimental conductance values (μS).Source EDV ESV FDM Model @ 10 kHz 1419 μS 844 μS Experiment @ 10 kHz1600 (500) 1300 (400) FDM Model @ 100 kHz 1493 905 Experiment @ 100 kHz2100 (400) 1700 (400) Experimental data are the means of six normal mice[28], numbers in parentheses are standard deviations.

The 100 kHz measurements reveal an additional effect due to the complexnature of the electrical properties of muscle and the effect ofcapacitance between the wires in the conductance (admittance) catheter12. While the actual values of the calculated conductance are subject tomany uncertainties, the differences between 10 kHz and 100 kHz values inthe model are due only to the electrical properties of muscle. So, inTable 1 it looks at first glance as though the model work has severelyunderestimated the capacitive effects in muscle. However, it must benoted that the reported in vivo measurements do not compensate out thestray capacitance in the catheter 12 at 100 kHz. At this point, it isnot clear precisely how much of the apparent frequency-dependent signalis due to catheter 12 capacitance, and how much is due to muscle signalin those data.

The improved muscle parallel conductance compensation techniquedescribed can be implemented in existing conductance machines either inembedded analysis software (real-time or off-line processing of measureddata) or in dedicated Digital Signal Processing hardware devices.

Phase Angle Measurement: There is an embedded difficulty in thismeasurement which must be addressed: the parasitic capacitance of thecatheters has effects on the measured admittance signal phase angle inaddition to the muscle permittivity component. One necessarily measuresthe two together; and a method for compensating out or otherwise dealingwith the catheter-induced effects is required. Fortunately, all of thenecessary catheter 12 characteristics can be measured a priori. We haveidentified three approaches to this problem.

First, the catheter, 12 phase angle effects stem from parasiticcapacitance between electrode wires in the catheter 12. The tetrapolarcase is relatively easy to discuss, and the multi-electrode cathetersconsist of several repeated combinations of the 4-electrode subunit. Wecan measure the six inter-electrode parasitic capacitances of the4-electrode systems (FIG. 4). The effect of the inter-electrodecapacitances can be reduced to a single capacitive admittance inparallel with the tissues, C_(cath), much larger than any of the C_(ij).This can be seen in experimental measurements on saline which has noobservable permittivity effects at frequencies below about 200 MHz;thus, all capacitance information (frequency-dependent increase in |η|,where η=σ+jω∈) in the signal comes from catheter 12 effects (FIG. 5). InFIG. 5 a small conductivity measurement probe (inter-electrodecapacitances from 60 to 70 pF) has been used to measure the apparentconductivity (|η|) of saline solutions between 720 μS/cm (lowest line)and 10,000 μS/cm (highest line). The lines cross because the point whereσ_(NaCl)=σ_(cath) moves to higher frequency for higher σ. C_(cath) isapproximately 1.5 nF here.

Second, a lumped-parameter circuit model can be constructed for catheter12 effects and use this model to correct the measured potential, ΔV, tothe value it would have in the absence of the parasitic capacitances.Third, we can advance the measurement plane from the current-sourceoutput, I_(s), (FIG. 5) and voltage measurement location, ΔV, to theoutside surfaces of the four electrodes 18 using a bilinear transform.This is a standard approach in impedance measurement [see ref. 14, Ch.5] and requires only a measurement at open circuit, short circuit and anormalizing load (say, 1 kΩ) to accomplish.

The first approach is the most practical for implementation in aclinical instrument: we will subtract the catheter 12 capacitance,C_(cath), (measured a priori) from the total capacitance of themeasurement, CtOt, with the remainder: C_(muscle)=C_(tot)−C_(cath). Themeasurement from 2 to 10 kHz includes only the real parts:Y₁₀=G_(b)+G_(musc). At 100 kHz:Y₁₀₀=G_(b)+G_(musc)+jω(C_(cath)+C_(musc)). Negative values are rejectedand C_(cath) is deterministic and not time-varying. The calculationstrategy is then: C_(tot)=|Y₁₀₀| sin(θ_(tot))/ω;C_(musc)=C_(tot)−C_(cath); finally,G_(p)=G_(musc)=σ_(m)C_(musc)/∈_(musc) (from the well knownconductance-capacitance analogy [40]) and G_(p) can be subtracted from|Y₁₀| to determine G_(b)—i.e. |Y₁₀|=G_(b)+G_(p). A purely analogapproach to this measurement is impossible, and a mixed signal approachwith extensive digital processing required for both catheter 12compensation and phase measurement is used. Based on the model trendsand measured values of Table 1, it is estimated the relative phaseangles in the measured admittance ought to be approximately 4° for EDVand 8° for ESV. The larger phase angle for ESV reflects the change inrelative proximity of the LV wall.

The non uniformity of the electrode sensing field is inherent in thesingle current source electrode geometry of FIG. 1. Two limiting casesillustrate the origin of this. First, for a sufficiently large cuvetteor blood volume, the electric and current density fields surroundingelectrodes 1 and 4 are similar in overall shape to those of a currentdipole: the magnitude of the current density decreases with the cube ofthe radius. At very large volume the voltage measured between electrodes2 and 3 is insensitive to the location of the outer boundary.Consequently, the measured conductance saturates at large volumes sincethe sensitivity, ΔG/ΔVol=0, and thus α=zero. Second, the other limit isreached when the outer radius of the volume is minimally larger than thecatheter 12 itself. In that case the current density approaches auniform distribution and α approaches 1. Radii between these limitscross over from α=1 to α=0.

The behavior of α was studied in experiments and numerical models of amouse-sized 4-electrode conductance catheter 12 in a volume-calibrationcuvette. This catheter 12 has L=4.5 mm between the centers of electrodes2 and 3 and is 1.4 F (i.e. 0.45 mm in diameter). The cuvette was filledwith 1M saline solution (σ=1.52 S/m at room temperature). The resultsare summarized in FIG. 3. In the Figure, “Ideal G” is the line α=1. Thenumerically calculated (squares) and measured (circles) conductance inμS are plotted vs. cuvette volume (μl). The measurement sensitivity,ΔG/ΔVol, in the figure=α(σ/L²), and this slope asymptotically approaches0 for volumes greater than about 150 μl for this catheter 12. Thisbehavior is determined solely by the geometry of the current densityfield, and α is independent of the conductivity of the solution.

Based on the numerical model and experimental results, a new calibrationequation using β(G) as the geometry calibration function to replace a inequation 4:

$\begin{matrix}{{{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}} & (4)\end{matrix}$

where: β(G)=the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L isdistance between measuring electrodes, and Y_(p)=the parallel “leakage”admittance, dominated by cardiac muscle. At small volumes, β(G)=α=1. Atlarge volumes, β(G) increases without bound, as expected from the modelwork in FIG. 6. The new calibration function includes the non-linearnature of the volume calculation: since for a particular catheter β(G)depends on the conductivity of the liquid and on measured G—i.e. oncuvette and/or ventricular blood outer radius—it is not simplyexpressible in terms of 1/α. The expression for β(G) for the mouse-sizedcatheter 12 described above for FIG. 6 data is:

β(G)(σ=0.928S/m)=1+1.774(10^(7.481×10) ⁻⁴ ^((G−2057)))  (5)

where: G is the measured conductance (S), the calculations have beencorrected to the conductivity of whole blood at body temperature (0.928S/m), and 2057 is the asymptotic conductance in μS when the cuvette isfilled with a large volume of whole blood. Here β(G) depends only on thereal part of Y because the cuvette measurements do not contain muscle.In use, G is the real part of [Y(t)−Y_(p)], and any imaginary part ofthe signal is rejected since it must come from a muscle component, orfrom the instrumentation. As required, β(G) approaches 1 as G becomessmall compared to the asymptote, 2057 μS.

The improved calibration method can be implemented in existingconductance machines either in embedded analysis software (real-time oroff-line processing of measured data) or in dedicated Digital SignalProcessing hardware devices.

Complex admittance in regard to overall admittance as it relates toY(t)−Y_(p) is as follows.

Y(t)=Gb+Gm+jωCm

Y _(p) =Gm+jωCm(Y _(p))

C_(m)=capacitance component of muscle (F=Farads) (C_(m))

ω=angular frequency (radians/second) (ω=2πf)

Gm=conductance of muscle (S=Siemens) (G_(m))

Gb=conductance of blood (S) (G_(b))

Y(t)=total instantaneous measured admittance (S) (after catheter 12effects have been compensated.

Y_(p)=total parallel admittance (everything but blood). The cardiacmuscle dominates Y_(p); and thus once Y_(p) is known (from themeasurement of phase angle—only muscle has capacitance and contributesto the phase angle) the estimate of G_(b) can be improved and thus thevolume of blood.

The following elaborates on the nonlinear relationship β(G) betweenconductance and volume.

1. Physical Principle:

β(G) is a nonlinear function for every admittance (conductance) catheter12. The function depends on the number, dimensions and spacing of theelectrodes 18 used, and on the electrical conductivity of the mediumwhich it is in. β(G) is determined by the shape of the current fieldcreated by the electrodes 18.

2. Experimental Determination

β(G) may be determined experimentally for any conductance catheter 12 incylindrical “cuvettes” in which a solution of known electricalconductivity is measured over a range of cuvette diameters. The “volume”is the volume of solution between the voltage sensing electrodes 18.

3. Determination by Solution of the Electric Field Equations

β(G) may also be determined by solving the governing electric fieldequations, namely Gauss' Electric Law—either in integral form or in theform of the Laplace at low frequency, and the wave equations at highfrequency—subject to appropriate boundary conditions. The solution maybe by analytical means (paper and pencil) or by numerical means, as in adigital computer 24 model of the electric and/or electromagnetic fields.For any current field established by two or more electrodes 18 a modelyields the measured conductance when the total current—surface integralof (sigma mag(E) dot product dS), where dS is the elemental area—isdivided by the measurement electrode voltage, from the model orcalculation results. Many books on electromagnetic field theory teachhow to make the calculation. A specific reference is Chapter 6 (p. 184)in W. H. Hayt and J. A. Buck “Engineering Electromagnetics”, 6th EditionMcGraw-Hill, Boston, 2001, incorporated by reference herein. Thespecific reference teaches how to calculate resistance, R, butconductance, G is simply the reciprocal of R, G=1/R. The calculated Gmay be a complex number (for mixed materials like tissues), in whichcase the catheter 12 measures “admittance”, Y, a complex number.

(A) Measured Conductance and Capacitance Signals

Two of the catheter electrodes (#1 and #4) are used to establish acurrent field in the ventricle. The current field results in an electricfield in the tissues, the strength of which is determined by measuringthe voltage between electrodes #2 and #3. Because electrodes 2 and 3carry negligible amounts of current, they provide a useful estimate ofthe electric field in the tissues. The current supplied to the tissue(electrodes 1 and 4) is divided by the voltage measured betweenelectrodes 2 and 3 to determine the admittance of the tissue, Y (S). Theadmittance consists of two parts, the Conductance, G (S) the real part,and the Susceptance, B (S), the imaginary part: Y=G+jB. In thismeasurement, both blood and muscle contribute to the real part of themeasured signal, G=G_(b)+G_(musc). However, after all catheter-inducedeffects have been removed, only the muscle can contribute to theimaginary part, B=jωC_(musc).

For any geometry of electric field distribution in a semiconductingmedium, the conductance may be calculated from:

$\begin{matrix}\begin{matrix}{G = \frac{I}{V}} \\{= \frac{\underset{S}{\int\int}\sigma \; {E \cdot {S}}}{- {\int_{a}^{b}{E \cdot {l}}}}}\end{matrix} & (a)\end{matrix}$

where the surface, S, in the numerator is chosen to enclose all of thecurrent from one of the electrodes used to establish the electric field,E, and the integration pathway in the denominator is from the lowvoltage “sink” electrode at position “a” to the higher voltage “source”electrode at position “b”. Similarly, for any geometry of electric fieldin a dielectric medium, the capacitance may be calculated from:

$\begin{matrix}\begin{matrix}{C = \frac{Q}{V}} \\{= \frac{\underset{S}{\int\int}ɛ\; {E \cdot {S}}}{- {\int_{a}^{b}{E \cdot {l}}}}}\end{matrix} & (b)\end{matrix}$

B) Parallel Admittance in the Cardiac Muscle

The measured tissue signal, Y=G_(b)+G_(musc)+jωC_(musc). From the highfrequency measurement C_(musc) may be determined from the measured phaseangle by: C_(musc)=|Y| sin(θ)/ω after catheter phase effects have beenremoved. By equations (a) and (b) above, the muscle conductance can bedetermined from its capacitance by: G_(musc)=σ/eC_(musc) since the twoequations differ only by their respective electrical properties—i.e. theelectric field geometry calculations are identical in a homogeneousmedium. In this way, the muscle conductance (independent of frequency,and thus the same in the low frequency and high frequency measurements)may be determined from the muscle capacitance (observable only in thehigh frequency measurements).

Beyond these very general relations, a person may make catheterelectrode configurations of many shapes and sizes and use them in manysorts of conductive solutions. All would have a different β(G) function.

In an alternative embodiment, the LV and/or RV volume signal is onlyrelative to LV or RV blood conductance, but the measured admittancecomes from both blood and myocardium. Therefore, it is desired toextract the blood conductance from the measured admittance, which can bedone by using the unique capacitive property of myocardium. To achieveit, the first step is to obtain the conductivity and permittivity ofmyocardium.

Myocardial Conductivity and Permittivity

It is believed that blood is only conductive, while myocardium is bothconductive and capacitive. Therefore, the measured frequency-dependentmyocardial “admittivity”, Y′_(m)(f), actually is composed of twocomponents:

Y′ _(m)(f)=√{square root over (σ_(m) ²+(2πf∈ _(r)∈₀)²)}  (6)

where σ_(m) is the real myocardial conductivity, f is frequency, ∈_(r)is the relative myocardial permittivity, and ∈₀ is the permittivity offree space. Experimentally, Y′_(m)(f) can be measured at two differentfrequencies, such as 10 and 100 kHz, and then the value of σ_(m) andmyocardial permittivity ∈ can be calculated by:

$\begin{matrix}{\sigma_{m} = \sqrt{\frac{{100 \cdot \left\lbrack {Y_{m}^{\prime}\left( {10\; k} \right)} \right\rbrack^{2}} - \left\lbrack {Y_{m}^{\prime}\left( {100k} \right)} \right\rbrack^{2}}{99}}} & (7) \\\begin{matrix}{ɛ \equiv {ɛ_{r}ɛ_{0}}} \\{= {\frac{1}{2{\pi \cdot 10^{4}}}\sqrt{\frac{\left. {Y_{m}^{\prime}\left( {100\; k} \right)} \right\rbrack^{2} - \left\lbrack {Y_{m}^{\prime}\left( {10\; k} \right)} \right\rbrack^{2}}{99}}}}\end{matrix} & (8)\end{matrix}$

Alternatively, Y′_(m)(f) can be measured at a single frequency, such as30 kHz, and then the value of am and myocardial permittivity can becalculated.

Blood Conductance

In the 10 and 100 kHz dual-frequency measurement system, the measuredmagnitude of admittance, |Y(f)|, is blood conductance (g_(b)) inparallel with myocardial conductance (g_(m)) and capacitance (C_(m)),shown as

|Y(10k)|=√{square root over ((g _(b) +g _(m))²+(2π·10⁴ C _(m))²)}{squareroot over ((g _(b) +g _(m))²+(2π·10⁴ C _(m))²)}  (9)

|Y(100k)|=√{square root over ((g _(b) +g _(m))²+(2π·10⁵ C_(m))²)}{square root over ((g _(b) +g _(m))²+(2π·10⁵ C _(m))²)}  (10)

Using equations (9) and (10),

$\begin{matrix}{C_{m} = {\frac{1}{2{\pi \cdot 10^{4}}}\sqrt{\frac{{{Y\left( {100k} \right)}}^{2} - {{Y\left( {10\; k} \right)}}^{2}}{99}}}} & (11) \\{{g_{b} + g_{m}} = \sqrt{\frac{{100 \cdot {{Y\left( {10\; k} \right)}}^{2}} - {{Y\left( {100\; k} \right)}}^{2}}{99}}} & (12)\end{matrix}$

From the well known conductance-capacitance analogy [40],

$\begin{matrix}{g_{m} = {C_{m}\frac{\sigma_{m}}{ɛ}}} & (13)\end{matrix}$

Substitute eq. (13) into eq. (12), blood conductance g_(b) is obtainedas

$\begin{matrix}{g_{b} = {\left( \sqrt{\frac{{100 \cdot {{Y\left( {10\; k} \right)}}^{2}} - {{Y\left( {100\; k} \right)}}^{2}}{99}} \right) - g_{m}}} & (14)\end{matrix}$

A new conductance-to-volume conversion equation is

Vol(t)=ρ_(b) L ² g _(b)(t)exp[γ·(g _(b)(t))²]  (15)

where Vol(t) is the instantaneous volume, τ_(b) is the bloodresistivity, L is the distance between the sensing electrodes, g_(b)(t)is the instantaneous blood conductance, and γ is an empiricalcalibration factor, which is determined by the following steps.

-   -   1. A flow probe is used to measure the LV stroke volume (SV),        denoted as SV_(flow).    -   2. Assign an initial positive number to γ, and use equation (15)        to convert blood conductance to volume signal. The resulting        stroke volume is denoted as SVγ.    -   3. If SVγ is smaller than SV_(flow) increase the value of γ.        Otherwise, decrease it.    -   4. Repeat steps 2 and 3 until it satisfies.

SVγ−SV_(flow)  (16)

-   -   Since equation (15) is a monotonic increasing function, there is        only one possible positive solution for γ.

This empirical factor γ is used to compensate and calibrate the overalluncertainty and imperfection of the measurement environment, such asinhomogeneous electrical field and off-center catheter position.

Simulation Results

A commercial finite element software, FEMLAB, is used to simulate thisproblem. A simplified LV model is created by modeling both LV blood andmyocardium as cylinders with a four-electrode catheter inserted into thecenter of cylinders, as shown in FIG. 8. A similar model could be madefor the RV as well.

The radius of the inner blood cylinder was changed to explore therelationship between volume and conductance. Assuming stroke volume isthe difference between the largest and smallest blood volume, and thisdifference is used to determine the empirical calibration factors, α andγ, for Baan's and the new equations respectively. The calculatedmagnitude of admittance, blood conductance, true volume, and estimatedvolume by Baan's and the new equations are listed in Table II and alsoplotted in FIG. 9, where the true volume is the volume between the twoinner sensing electrodes. The distance between two inner sensingelectrodes for a mouse size catheter is 4.5 mm.

TABLE II Comparison of true and estimated volume by two equationsCalculated Estimated Estimated magnitude of Blood True volume by volumeby admittance conductance volume Baan's equation new equation (μS) (μS)(μL) (μL) (μL) 2491.1 2344.7 62.9 64.5 62.0 2030.2 1853.3 43.7 51.0 43.11514.0 1314.3 28.0 36.2 27.5 1337.7 1133.5 23.5 31.2 23.0 1162.4 956.119.4 26.3 19.0 992.5 786.4 15.7 21.6 15.3 829.3 626.2 12.4 17.2 12.0677.3 479.3 9.5 13.2 9.1 538.1 347.9 7.0 9.6 6.6 414.4 234.2 4.9 6.4 4.4

In Vitro Saline Experiments

Several cylinder holes were drilled in a 1.5-inch thick block ofPlexiglas. The conductivity of saline used to fill those holes was 1.03S/m made by dissolving 0.1 M NaCl in 1 liter of water at 23° C. roomtemperature, which is about the blood conductivity. A conductancecatheter with 9 mm distance between electrodes 2 and 3 is used tomeasure the conductance.

Since plexiglas is an insulating material, the measured conductancecomes from saline only, not from the plexiglas wall. Therefore, themeasured saline conductance corresponds to the blood conductance in vivoexperiments. Again, stroke volume is assumed to be the differencebetween the largest and smallest blood volume, and then used todetermine the empirical calibration factors, α and γ, for Baan's and thenew equations, respectively. The measured data at 10 kHz and theestimated volume by Baan's and the new equations are listed in TableIII. The true volume listed is the volume between electrodes 2 and 3.The data are plotted in FIG. 10.

TABLE III Comparison of true and estimated volume in the drilled holesEstimated Estimated Diameter of Measured True volume by volume byDrilled holes conductance volume Baan's equation new equation (inch)(μS) (μL) (μL) (μL)   3/16 1723.5 160.3 562.0 160.5 ¼ 2675.0 285.0 872.3310.3   5/16 3376.0 445.3 1100.9 494.5 ⅜ 3836.4 641.3 1251.0 684.8  7/16 4171.0 827.9 1360.1 866.7 ½ 4394.3 1140.1 1432.9 1031.2

It is found that the resulting volumes obtained from the new equationare much closer to the MRI data, which is believed to be the truth.However, more noise is found in a larger volume by the new method. Thereason is that as the volume increases, the exponential term of the newequation would amplify the noise more rapidly than the linear Baan'sequation.

The following applications are based on the above explanation.

The present invention pertains to an apparatus 500 for determining hearttransplant rejection of a heart in a patient, as shown in FIGS. 11-15.The apparatus 500 comprises at least two electrodes 502 adapted to besewn into the heart that span the left ventricle. The apparatus 500comprises a voltage generator 504 adapted to be inserted in the patientwhich generates a voltage to the two electrodes 502 and senses theresulting voltage from the two electrodes 502.

Preferably, the apparatus 500 includes a third electrode 506 and afourth electrode 508 adapted to be implanted in the LV myocardium, andwherein the voltage generator 504 determines both the magnitude andphase angle of the resulting voltage from the two, electrodes 502 andthe third and fourth electrodes. The voltage generator 504 is preferablyadapted to be implanted in the chest of the patient and is incommunication with the two electrodes 502 and the third and fourthelectrodes.

The present invention pertains to a method for determining hearttransplant rejection of a heart in a patient. The method comprises thesteps of sewing into the heart at least two electrodes that span theleft ventricle. There is the step of inserting in the patient a voltagegenerator which generates a voltage to the two electrodes and senses theresulting voltage from the two electrodes.

The present invention pertains to a pacemaker 600 for a patient, asshown in FIG. 18. The pacemaker will include traditional pacemakers forslow heart rates, bi-ventricular pacemakers to improve LV and RVsynchrony for heart failure patients, and AICD devices with both pacingand defibrillation functions. The pacemaker 600 comprises an RV lead 602having four electrodes 604 that span the length of the RV adapted to beinserted at the RV apex with at least one of the four electrodes placedin either the right atrium or veins drawing into the right heart of thepatient. The pacemaker 602 comprises a voltage generator 606 whichgenerates a voltage signal to the electrodes 604 and senses theinstantaneous voltage in the RV and determines the real and imaginarycomponents to remove the myocardial component from the septum and RVfree wall to determine absolute RV blood volume. The pacemaker 600comprises a battery 608 connected to the voltage generator 606. Thepacemaker 600 comprises a defibrillator 610 connected to the battery608.

Preferably, the pacemaker 600 includes a surface epicardial catheter 612having four electrodes 614.

The present invention pertains to a method for assisting a heart of apatient. The method comprises the steps of inserting into the RV apex anRV lead of a pacemaker having four electrodes that span the length ofthe RV. There is the step of generating a voltage signal to theelectrodes from a voltage generator. There is the step of sensing theinstantaneous voltage in the RV with the voltage generator to determinethe real and imaginary components of the voltage to remove themyocardial component from the septum and RV free wall to determineabsolute RV blood volume.

More specifically, in regard to a non-invasive method and apparatus todetermine heart transplantation rejection, patients undergoing hearttransplantation continue to be routinely referred for invasivemyocardial biopsy for histologic examination to determine if rejectionis occurring to guide dose adjustment of immunosuppressive medications.This invasive method subjects patients to morbidity and random samplingerrors. Previous noninvasive methods 11-14 have been studied and havebeen unsuccessful. Electrical Admittance of myocardial tissue can beused to identify transplant rejection 15. The presence of infiltratinglymphocytes, membrane injury and edema decreases electrical Admittancein the myocardium. An important contributor to the myocardial Admittanceis myocyte membrane capacitance. As myocytes are damaged by the processof rejection, the capacitance will be reduced. A device attached to thehealthy heart as it is transplanted, which will be monitored forrejection by telemetry can reveal the rejection process, as shown inFIGS. 11-15.

At the time of heart transplantation, the healthy heart that will beplaced into the chest of the patient will have 2 to 4 electrodes sewninto the heart that span the left ventricle. These electrodes will beattached to a device that can be inserted within the chest cavity thatwill generate a voltage to two of these electrodes, then sense theresulting voltage with either the identical two electrodes, orelectrodes 3 and 4 implanted in the LV myocardium and determine both themagnitude and phase angle of this returning signal. This device willhave the capability to generate these myocardial measurements bytelemetry to either a doctor's office or hospital. If the baselineresistivity of the myocardium is changing, especially the phase angle,then it will be interpreted to mean that myocardial rejection of the newheart is occurring. The patient's doctor will use this information todetermine if the patient's dose of anti-rejection medications such assteroids need to be increased. Alternatively, if the resistivity of theheart returns to a safe range, then increased anti-rejection medicationscan be reduced. FIGS. 11-15 show two embodiments regarding thistechnique. In one embodiment, as shown in FIG. 12, a penetratingtransducer 512 having the electrodes is inserted into the heart. In asecond embodiment, a surface transducer 514 is sewn to the surface ofthe heart. FIG. 15 shows the various embodiments in application. Onlyone embodiment would be used at a time. FIGS. 16 and 17 show differentplacements regarding the apparatus 500.

FIG. 11 shows the penetrating transducer that is inserted into thetransplanted heart. The electrodes would be disposed inside the heartwith the stopper contacting the heart surface and preventing thepenetrating transducer from extending further into the heart.

FIGS. 12 and 13 show a bottom view and a side view, respectively, of thesurface transducer that would be attached to the surface of thetransplanted heart. The electrodes are found on the surface transducer.

FIG. 14 shows the electric field lines about either the penetratingtransducer or the surface transducer. It should be noted that while thepenetrating transducer and the surface transducer are both showntogether with the transplanted heart in FIG. 14, in reality, only one ofthe embodiments would be used. The presence of both transducers issimply for exemplary purposes. Similarly, FIG. 15 shows the surfacetransducer attached to the epicardium, or the penetrating catheterinserted either endocardially or epicardially. In practice, only onetransducer would actually be used.

Variations of this device can include a hand held device that is appliedto the closed chest wall, to activate the electrodes in the chest tosave on battery usage. The device in the chest can also utilize themotion of the heart to self generate energy as well, by translating thetorsional motion of the heart into electric energy.

Another application, as shown in FIG. 18, is the determination of RVvolume coupled to a pacemaker/defibrillator lead 602 in the RV. AICD arenow recommended in any heart failure patient with an LVEF of less than30%. There is also an effort to reduce hospital admissions for patientsdue to episodes of CHF by detecting right heart pressures to alert thepatient that they are going into fluid overload before the clinicalentity of CHF occurs. Since the right and left ventricularpressure—volume relations during filling (diastole) are relatively flat,there is a large change in volume for a small change in pressure. Hence,detecting RV volume accurately will be a more sensitive marker of thedevelopment of impending CHF than will be RV or pulmonary arterypressure, or trans-lung impedance the latter an indirect measure ofpulmonary edema. Thus, the placement of 4 electrodes on the RV lead thatspan the length of the RV of a AICD/pacemaker to be implanted in apatient with a reduced LVEF coupled with phase angle (the functiongenerator board placed in the battery—circuit of the device) to provideinstantaneous RV volume via telemetry can be used to generate the goldstandard for impending heart failure, instantaneous RV volume.

The AICD lead 602 that is in the right ventricle and inserted into theRV apex has 2 to 4 electrodes 604 mounted on it. The AICD battery 608that is already implanted under the skin can also be used to thengenerate a voltage signal between electrodes 1 and 4 on the RV lead 602,and sense the instantaneous voltage in the RV and determine the real andimaginary components to remove the myocardial component of the septumand RV free wall to determine absolute RV blood volume. The additionalelectronic circuits for phase angle can be added to the device alreadyimplanted under the skin as well.

The patient at home can via telemetry send to their doctor the phaseangle information from the RV chamber, and determine if the RV volume isincreasing or not. If it has increased, before the patient has hadsymptoms of congestive heart failure, then the patient's medications canbe altered to remove fluid (diuresis) in order to avoid futurehospitalization.

RV volume will be more sensitive that telemetric RV pressure since asthe RV dilates, it maintains a similar pressure. It will also be incompetition with a device made by Medtronic, Inc., which determines theimpedance of the entire chest as an indirect method to determine if thelungs are filling with fluid (pulmonary edema) before the patient needsto be hospitalized with congestive heart failure. The Medtronic deviceis limited because it is determining impedance not only of the lungs,but the entire chest wall.

Although the invention has been described in detail in the foregoingembodiments for the purpose of illustration, it is to be understood thatsuch detail is solely for that purpose and that variations can be madetherein by those skilled in the art without departing from the spiritand scope of the invention except as it may be described by thefollowing claims.

The following is a list of references, identified herein, all of whichare incorporated by reference herein.

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1. An apparatus for determining heart transplant rejection of a heart ina patient comprising: at least two electrodes adapted to be sewn intothe heart that span the left ventricle; and a voltage generator adaptedto be inserted in the patient which generates a voltage to the twoelectrodes and senses the resulting voltage from the two electrodes. 2.An apparatus as described in claim 1 including a third electrode and afourth electrode adapted to be implanted in the LV myocardium, andwherein the voltage generator determines both the magnitude and phaseangle of the resulting voltage from the two electrodes and the third andfourth electrodes.
 3. An apparatus as described in claim 2 wherein thevoltage generator is adapted to be implanted in the chest of the patientand is in communication with the electrodes.
 4. An apparatus asdescribed in claim 3 wherein the voltage regulator includes a processor.5. An apparatus as described in claim 4 including a pressure sensor formeasuring instantaneous pressure of the heart chamber in communicationwith the processor.
 6. An apparatus as described in claim 5 wherein theprocessor produces a single wave form at a desired frequency for theconductance (admittance) catheter.
 7. An apparatus as described in claim6 wherein the processor produces a plurality of desired wave forms atdesired frequencies for the conductance (admittance) catheter.
 8. Anapparatus as described in claim 7 wherein the processor produces theplurality of desired wave forms at desired frequencies simultaneously,and the processor separates the plurality of desired wave forms atdesired frequencies the processor receives from the conductance(admittance) catheter.
 9. An apparatus as described in claim 8 whereinthe conductance (admittance) catheter includes a plurality of electrodesto measure a least one segmental volume of a heart chamber.
 10. Anapparatus as described in claim 9 wherein the non-linear relationshipdepends on a number of the electrodes, dimensions and spacing of theelectrodes, and an electrical conductivity of a medium in which theelectrodes of the catheter are disposed.
 11. An apparatus as describedin claim 10 wherein the non-linear relationship isβ(G)(σ=0.928S/m)=1+1.774(10^(7.481×10) ⁻⁴ ^((G−2057))) where: G is themeasured conductance (S), the calculations have been corrected to theconductivity of whole blood at body temperature (0.928 S/m), and 2057 isthe asymptotic conductance in uS when the cuvette is filled with a largevolume of whole blood.
 12. An apparatus as described in claim 11 wherein${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$where: β(G) the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, c is blood conductivity, L isdistance between measuring electrodes, and Y_(p)=the parallel leakageadmittance, dominated by cardiac muscle.
 13. An apparatus as describedin claim 12 wherein the pressure sensor is in contact with theconductance catheter to measure ventricular pressure in the chamber. 14.An apparatus as described in claim 13 wherein the plurality ofelectrodes includes intermediate electrodes to measure an instantaneousvoltage signal from the heart, and outer electrodes to which a currentis applied from the processor.
 15. An apparatus as described in claim 14wherein the pressure sensor is disposed between the intermediateelectrodes and the outer electrodes.
 16. An apparatus as described inclaim 15 wherein the processor includes a computer with a signalsynthesizer which produces the plurality of desired wave forms atdesired single or multiple frequencies and a data acquisition mechanismfor receiving and separating the plurality of desired wave forms atdesired frequencies.
 17. An apparatus as described in claim 16 whereinthe computer converts conductance into a volume.
 18. An apparatus asdescribed in claim 17 wherein the computer produces a drive signalhaving a plurality of desired wave forms at desired frequencies to drivethe conductance catheter.
 19. An apparatus as described in claim 10whereinVol(t)=ρL ² g _(b)(t)exp[γ*(g _(b)(t))²] where Vol(t) is theinstantaneous volume, ρ is the blood resistivity, L is the distancebetween the sensing electrodes, g_(b)(t) is the instantaneous bloodconductance, and γ is an empirical calibration factor.
 20. A pacemaker,including bi-ventricular pacemaker and AICDS, for a patient comprising:an RV lead having four electrodes spanning the length of the RV adaptedto be inserted into the RV apex with at least one of the four electrodesplaced in either the right atrium or veins draining into the right heartof the patient; a voltage generator which generates a voltage signal tothe electrodes and senses the instantaneous voltage in the RV anddetermines the real and imaginary components to remove the myocardialcomponent of the septum and RV free wall to determine absolute RV bloodvolume; a battery connected to the voltage generator; a defibrillatorconnected to the battery; and a bi-ventricular pacemaker toresynchronize RV and LV ventricular contraction.
 21. A method fordetermining heart transplant rejection of a heart in a patientcomprising the steps of: sewing into the heart at least two electrodesthat span the left ventricle; and inserting in the patient a voltagegenerator which generates a voltage to the two electrodes and senses theresulting voltage from the two electrodes.
 22. A method as described inclaim 21 including the step of measuring instantaneous pressure of theheart chamber with a pressure sensor in communication with a processorof the voltage regulator.
 23. A method as described in claim 22including the step of producing a plurality of desired wave forms atdesired frequencies for the conductance (admittance) catheter.
 24. Amethod as described in claim 23 wherein the producing step includes thestep of producing a single waveform at a single frequency.
 25. A methodas described in claim 23 wherein the producing step includes the step ofproducing the plurality of desired wave forms at desired frequenciessimultaneously, and including the step of the processor separating theplurality of desired way forms at desired frequencies the processorreceived from the conductance (admittance) catheter.
 26. A method asdescribed in claim 25 wherein the producing step includes the step ofproducing with the processor the plurality of desired wave forms atdesired frequencies simultaneously.
 27. A method as described in claim26 wherein the determining step includes the step of applying thenon-linear relationship according toβ(G)(σ=0.928S/m)=1+1.774(10^(7.481×10) ⁻⁴ ^((G−2057))) where: G is themeasured conductance (S), the calculations have been corrected to theconductivity of whole blood at body temperature (0.928 S/m), and 2057 isthe asymptotic conductance in μS when the cuvette is filled with a largevolume of whole blood.
 28. A method as described in claim 27 wherein thedetermining step includes the step of determining instantaneous volumeaccording to${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$where: β(G) the field geometry calibration function (dimensionless),Y(t)=the measured combined admittance, and Y_(p)=the parallel leakageadmittance, dominated by cardiac muscle.
 29. A method as described inclaim 28 wherein the step of measuring instantaneous pressure includesthe step of measuring instantaneous pressure with the pressure sensor incontact with the conductance (admittance) catheter to measure theventricular pressure in the chamber.
 30. A method as described in claim29 wherein the measuring step includes the step of measuring at leastone segmental volume of a heart chamber with a plurality of electrodeson the conductance catheter.
 31. A method as described in claim 30wherein the measuring step includes the steps of applying a current toouter electrodes of the plurality of electrodes from the processor, andmeasuring an instantaneous voltage signal from the heart withintermediate electrodes of the plurality of electrodes.
 32. A method asdescribed in claim 31 wherein the step of measuring instantaneouspressure includes the step of measuring instantaneous pressure with thepressure sensor disposed between the intermediate electrodes and theouter electrodes.
 33. A method as described in claim 32 wherein theproducing with the processor step includes the step of producing with asignal synthesizer of a computer a single wave form at a singlefrequency.
 34. A method as described in claim 33 wherein the producingwith the processor step includes the step of producing with a signalsynthesizer of a computer the plurality of desired wave forms at desiredfrequencies, and the processor separating step includes the step ofreceiving and separating the plurality of desired wave forms at desiredfrequencies with a data acquisition mechanism of the computer.
 35. Amethod as described in claim 34 including the step of convertingconductance (admittance) into a volume with the computer.
 36. A methodas described in claim 35 including the step of producing with thecomputer a drive signal having a wave form at a single frequency todrive the conductance (admittance) catheter.
 37. A method as describedin claim 36 including the step of producing with the computer a drivesignal having the plurality of desired wave forms at desired frequenciesto drive the conductance (admittance) catheter.
 38. A method asdescribed in claim 37 wherein the determining step includes the step ofdetermining instantaneous volume according toVol(t)=ρ_(b) L ² g _(b)(t)exp[γ·(g _(b)(t))²]  (15) where Vol(t) is theinstantaneous volume, σ_(b) is the blood resistivity, L is the distancebetween the sensing electrodes, g_(b)(t) is the instantaneous bloodconductance, and γ is an empirical calibration factor.
 39. A pacemakeras described in claim 20 including a surface epicardial catheter having4 electrodes.
 40. A method for assisting a heart of a patient comprisingthe steps of: inserting into the RV apex an RV lead of a pacemakerhaving four electrodes that span the length of the RV; generating avoltage signal to the electrodes from a voltage generator; and sensingthe instantaneous voltage in the RV with the voltage generator todetermine the real and imaginary components of the voltage to remove themyocardial component of the septum and RV free wall to determineabsolute RV blood volume.